For over two decades, computer algebra systems like Maple and Mathematica have been successfully used in the undergraduate curriculum to enhance students' understanding of calculus, linear algebra, and differential equations. These systems have matured and are used by researchers not only for rote calculations, but also in the discovery process. One now can use the computer to discover new mathematical patterns and relationships, create impressive graphics to expose mathematical structure, demonstrate that conjectures are false, confirm analytically derived results, and suggest approaches for formal proofs. This is the thrust of experimental mathematics, a growing paradigm that is revolutionizing how some mathematical research is being done today. Researchers use this approach to discover results in function representation, integration, dynamical systems, and number theory that would be difficult to prove without the intelligent use of computers.
Intellectual Merit: Very few graduate level courses are offered to teach experimental mathematics, and none at the undergraduate level. This goal of this project is to design an advanced undergraduate course that is teaching students fluency in a computer algebra system and adeptness at using the tools and approaches of experimental mathematics. It is also providing students a research experience immersed in the experimental approach. The project team is developing modules and sets of problems that are being posted on an experimental mathematics website.
Broader Impact: Training future mathematicians to understand the power of experimental mathematics is having a profound effect on mathematical progress. The project team is organizing sessions and workshops at national meetings to present materials and to build a broader community of faculty who support experimental mathematics courses. Colleagues at various other universities (Rutgers, Clemson, Brigham Young, Dalhousie, Loyola Marymount) are incorporating experimental mathematical materials developed by the project into their courses and providing feedback on content and impact. The project team has been involved in programs designed to increase the number of Chicanos/Latinos and Native Americans earning advanced degrees and pursuing research careers in the mathematical sciences. This project builds on that work to provide students from underrepresented groups an experience with experimental mathematics.
